News Corporation chairman and chief executive Rupert Murdoch has today challenged the "myth" that he has used his newspapers to influence the UK political establishment over the years.

Murdoch said that it was "untrue" that he was upset with Prime Minister David Cameron for setting up the Leveson Inquiry in the wake of the phone hacking scandal at the News of the World. Instead, he said that he welcomed the opportunity to "put some myths to bed".

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In evidence given under oath for around four hours, the 81-year-old billionaire answered questions on his relationship with British prime ministers over the past four decades.

Murdoch said that the perception of his all-powerful influence over politicians was wrong, and irritated him.

Asked at the inquiry by Robert Jay QC about the nature of recent meetings with Cameron, who Murdoch's The Sun endorsed ahead of the 2010 general election, Murdoch responded: "Mr Jay, you keep inferring that endorsements were motivated by business motives and if that had been the case we would have endorsed the Conservative Party in every election. But I didn't. I was interested in issues."

Jay pushed Murdoch on whether he had ever discussed the licence fee funding situation for the BBC, but Murdoch dismissed that outright, saying of politicians: "They all hated the BBC, and they all gave it what it wanted."

He said that he wanted to dispel the myth "once and for all" that he "used the influence of The Sun or the supposed political power to get favourable treatment".

Murdoch added: "Because I think it's a myth. And, everything I do every day I think proves it to be such. Have a look at - well it's not a problem - but how I treat Mayor Bloomberg in New York - sends him crazy. But, we support him every time he runs for re-election."

Murdoch detailed the implosion of his relationship with one former prime minister, Gordon Brown, when The Sun announced its shift of support to the Conservatives.

He quoted Brown as saying at the time: "Well, your company has declared war on my government and we have no alternative but to make war on your company."

Asked why the former Labour leader would say that, Murdoch replied: "I don't think that he was in a balanced state of mind."

The media mogul admitted that he regarded Tony Blair as a personal friend, and recalled the then-Labour leader speaking "convincingly about the ability of a new Labour Party to energise Britain" at a News Corp conference in 1995.

But in his written statement to the Leveson Inquiry, Murdoch said that Blair had not expressly asked him for support, and he had never asked anything of Blair.

"Mr Blair did not expressly request our support in 1995, 1997 or any other election, but he was a politician and I had no doubt that he would welcome the support of our newspapers and our readers," he said.

"I want to say that I, in 10 years of his power, never asked Mr Blair for anything."

Murdoch said that he first met Cameron when he was a leader of the Opposition, at a family picnic at his daughter's home, but they did not discuss politics.

He confirmed that he also met Cameron on various occasions after he became prime minister, but insisted these were "principally in social settings, where little of substance was discussed".

The News Corp boss was unable to recall whether it was his own or his daughter's yacht on which he met Cameron in August 2008 near the Greek island of Santorini.

The billionaire denied ever having discussed with Cameron News Corp's bid to acquire the 60.9% of UK broadcaster Sky that it did not already own.

He said that there was no link in his mind between his support for the Conservatives and News Corp's bid, despite Jay noting that the bid was submitted shortly after Cameron was elected prime minister in 2010.

In his session today, Murdoch was mostly calm and assured when giving evidence, although there were moments when he appeared to contradict himself, particularly over his efforts to exert editorial control over his newspapers.

At one stage, Murdoch said that he did not try to influence The Times, but later claimed that any politician who wants to know his political views should read the editorial in The Sun.

Murdoch said that he was "sorry to say" that he "never much interfered" with the News of the World, which was shut down last July at the height of the hacking affair.

He said that he tried to set an example of ethical behaviour for his employees, and noted that phone hacking or using private detectives was a "lazy way of reporters not doing their job".

However, he added: "I think it is fair when people have themselves held up as iconic figures or great actors that they be looked at."

In his witness statement in the inquiry, Murdoch confirmed that the Management and Standards Committee, the internal body set up by News Corp to clean up the hacking affair, is co-operating with the US Department of Justice.

This follows confirmation from lawyer Mark Lewis that he was in talks to represent up to four people who believe that their phones were hacked while on US soil.

Murdoch will appear again at the inquiry tomorrow at 10am to answer further questions.